To my untrained mind using two relays that way sounds dangerous since they're mechanical devices. What happens if they don't open fast enough and they generate an short? Boom!Isn't an H-Bridge used when one wants to control the polarity of current in an circuit?

You can use a Double Pole Double Throw relay. Look here for schematics: http://www.trainelectronics.com/Reverse_loop_dual_coil_relay/index.htm. Image no. 2 is with a DPDT relay, where the current is one way when the relay is activated and the other when no current flows through the relay. If you insist on the change to occur when the current through the relay is reversed and not just on/off, you can use diodes to block the current through the relay when the power is reversed, so the relay switches to the off state.

Lets go through the second drawing on the link I send you. Let's assume, that the button is not pressed and current is not flowing through the relay coil.

If you study the top part of the drawing, you can see two sets of contact sets. Lets call them 1 and 2. One is connected to + on the "From power supply", the other to -. Both contact sets have two contacts that are labelled N.C. and N.O. This stands for "Normally Closed" and "Normally Opened", meaning that if no power flows through the coil, the middle pin will touch the "Normally closed" pin.

Try to follow the current in the schematics. + from the battery goes to the contact set 1, through the top contact and to the topmost of the "To track" wires. (It could have read "To motor", but the site is about model railroads. This doesn't matter, the principle is the same). The - from the battery goes to the contact set 2, through the top contact and to the bottom of the "To track" wires.

Now, if we supply power to the relay coil, it will switch the two contact sets, so the two "angled" parts of the two contact sets will move to the bottom contact. If you imagine this and follow the power, you will see that + still flows to contact set 1, but since the contact is switched, it will go the the lower contact, labelled N.O. and to the lower of the "to track" wires. Likewise, - still goes to the second contact set, though the lower contact labelled N.O. and to the topmost "to track" wire.

The effect is, that when you supply power to the relay coil, the output "to track" will have + and - reversed.

I just made some quick drawings showing the current flow, when there is no current going through the relay (DPDTRelay.jpg) and when power flows through the relay (DPDTRelay2.jpg). It's edits of the drawing from the site I linked to. Note that the relay-coil part is not edited, only the part with the contact sets.

If you want the power to reverse, when you reverse the power to the relay, attach a diode to one of the pins on the relay coil. This will prevent power flowing to the relay if you reverse the power to the coil and that will make the power on the output reverse.